The effectiveness of a cardiovascular magnetic resonance (CMR) scan depends on the ability of the operator to correctly tune the acquisition parameters to the subject being scanned and on the potential occurrence of imaging artefacts such as cardiac and respiratory motion. In the clinical practice, a quality control step is performed by visual assessment of the acquired images: however, this procedure is strongly operatordependent, cumbersome and sometimes incompatible with the time constraints in clinical settings and large-scale studies. We propose a fast, fully-automated, learning-based quality control pipeline for CMR images, specifically for short-axis image stacks. Our pipeline performs three important quality checks: 1) heart coverage estimation, 2) inter-slice motion detection, 3) image contrast estimation in the cardiac region. The pipeline uses a hybrid decision forest method - integrating both regression and structured classification models - to extract landmarks as well as probabilistic segmentation maps from both long- and short-axis images as a basis to perform the quality checks. The technique was tested on up to 3000 cases from the UK Biobank as well as on 100 cases from the UK Digital Heart Project, and validated against manual annotations and visual inspections performed by expert interpreters. The results show the capability of the proposed pipeline to correctly detect incomplete or corrupted scans (e.g. on UK Biobank, sensitivity and specificity respectively 88% and 99% for heart coverage estimation, 85% and 95% for motion detection), allowing their exclusion from the analysed dataset or the triggering of a new acquisition.